1. Field of the Invention
The invention relates generally to the field of communications. More particularly, the invention relates to methods of multidimensional signal modulation and/or demodulation for data communications, and machinery for transmitting and/or receiving such communications.
2. Discussion of the Related Art
Currently available advanced RF modulation schemes in use typically incorporate multistate modulation schemes such as n-QAM, m-ary FSK, or m-ary PSK to accommodate higher rates of data transmission than are possible in standard binary (2-state) signaling techniques such as binary phase-shift keying (BPSK), simple on-off keying (OOK), or standard frequency-shift keying (FSK). The most spectrally efficient and robust techniques for a given modulation density are currently generally agreed in the art to be the rectangular n-QAM (quadrature amplitude modulation) constellations, where in general the number of equally spaced modulation states n is a binary power, 2k, where k=2, 3, 4, 5, 6, 7, 8, . . . Most often these systems utilize an even binary power, 22k, e.g., 4, 16, 64, or 256 modulation states. FIG. 24 shows a conventional constellation for 4-QAM with 2 bits per symbol. This same constellation can represent quadrature phase shift keying (QPSK or 4-PSK).
Theoretically, higher numbers of states are possible, but the practical constraints of required levels of linearity in the modulating circuitry and realizable signal-to-noise ratios (SNRs) in the transmission links and receiving hardware limit most current-day systems to a maximum density of 256 states (“256-QAM”). In addition, other constellation forms such as hexagonal may be useful in establishing more efficient coding schemes (i.e., increasing the mean Euclidean distances between adjacent points in the symbol constellations), although such hexagonal constellations may be more suitable for nonbinary codes (indicies other than two).
Techniques such as Trellis coding have also been employed to increase the effective difference between signal states representing adjacent coded data symbols by re-mapping the standard constellation of FIG. 24 into the modified form of FIG. 25. FIG. 25 shows a conventional constellation for 8-PSK. Note that the respective “Hamming” distances (discretized linear or Euclidean geometric distances between adjacent symbols as represented in the modulation constellations) are increased in the latter, thus realizing improved performance (i.e., lower data error rates for a given SNR condition) by using the Trellis coding.